Is there a way to "crudely" approximate PDEs with Fourier series?(adsbygoogle = window.adsbygoogle || []).push({});

By saying crudely, I meant this way:

Assuming I want a crude value for a differential equation using Taylor series;

y' = x + y, y(0) = 1

i'd take a = 0 (since initially x = 0),

y(a) = 1,

y'(x) = x + y; y'(a) = 0 + 1 = 1

y"(x) = 1 + y'; y"(a) = 1 + 1 = 2

y'"(x) = 0 + y"(x); y"'(a) = 0 + 2 = 2

then y ~ 1 + x + 2/2! x^2 + 2/3! x^3.

Or something similar to that. Does this crude method have an analog to Fourier-PDE solutions?

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# Crude Fourier Series approximation for PDEs.

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